Galois theory, functional Lindemann-Weierstrass, and Manin maps

We prove several new results of Ax-Lindemann type for semiabelian varieties over the algebraic closure K of C(t), making heavy use of the Galois theory of logarithmic differential equations. Using related techniques, we also give a generalization of the theorem of the kernel for abelian varieties over K.Comment: 37 page

"Soft" Anharmonic Vortex Glass in Ferromagnetic Superconductors

Ferromagnetic order in superconductors can induce a {\em spontaneous} vortex (SV) state. For external field ${\bf H}=0$, rotational symmetry guarantees a vanishing tilt modulus of the SV solid, leading to drastically different behavior than that of a conventional, external-field-induced vortex solid. We show that quenched disorder and anharmonic effects lead to elastic moduli that are wavevector-dependent out to arbitrarily long length scales, and non-Hookean elasticity. The latter implies that for weak external fields $H$, the magnetic induction scales {\em universally} like $B(H)\sim B(0)+ c H^{\alpha}$, with $\alpha\approx 0.72$. For weak disorder, we predict the SV solid is a topologically ordered vortex glass, in the ``columnar elastic glass'' universality class.Comment: minor corrections; version published in PR

Polaron Crystallization and Melting: Effects of the Long-Range Coulomb Forces

On examining the stability of a Wigner crystal in an ionic dielectric, two competitive effects due to the polaron formation are found to be important: (i) the screening of the Coulomb force, which destabilizes the crystal, compensated by (ii) the increase of the carrier mass (polaron mass). The competition between the two effects is carefully studied, and the quantum melting of the polaronic Wigner crystal is examined by varying the density at zero temperature. By calculating the quantum fluctuations of both the electron and the polarization, we show that there is a competition between the dissociation of the polarons at the insulator-to-metal transition (IMT), and a melting towards a polaron liquid. We find that at strong coupling, a liquid state of dielectric polarons cannot exist, and the IMT is driven by the polaron dissociation. Next, taking into account the dipolar interactions between localized carriers, we show that these are responsible for an instability of the transverse vibrational modes of the polaronic Wigner crystal as the density increases. This provides a new mechanism for the IMT in doped dielectrics, which yields interesting dielectric properties below and beyond the transition. An optical signature of such a mechanism for the IMT is provided.Comment: 10 pages, 3 figures, to be published in Int.J.Mod.Phys.

Papers: Contribution Letter Draft

Folder: Maud Gordon Holmes Arboretum. Edna Lindemann Corr. Proposal_

The intellectual and moral integrity of bioethics: response to commentaries on A case study in unethical transgressive bioethics: \u27Letter of concern from bioethicists\u27 about the prenatal administration of dexamethasone .

In our target article we showed that the Letter of Concern (LoC) fails to meet accepted standards for presenting empirical data for the purpose of supplementing a normative claim and for argument-based normative ethics. The LoC fails to meet the standards of evidence-based reasoning by making false claims, failing to reference data that undermine its key premises, and misrepresenting and misinterpreting the scientific publications it selectively references. The LoC fails to meet the standards of argument-based reasoning by treating as settled matters what are, instead, ongoing controversies, offering “mere opinion” as a substitute for argument, and making contradictory claims. The LoC is methodologically defective and thus a case study in unethical transgressive bioethics. Not withdrawing the LoC will damage the field of bioethics, making this case study in unethical transgressive bioethics important for the entire field